Tab indentations were useful for typewriters, and remain a feature of plain text editors. However, in a word processor, they are unreliable, especially when a document is being revised. Yet the dialogues for paragraph formatting continue to provide a tab for tab settings.
You can eliminate the most common of tab indentations—to mark the start of a new paragraph—by setting a First line indentation on the Indents and Spacing tab in the Paragraphs dialog, then selecting the Automatic box below it. For other tasks where indentations might be useful, such as headers or footers, a table with a single row and invisible borders generally positions text more accurately than tab indentations can.
The one feature in which tab indentations are unavoidable are tables of contents, which use them automatically.
Fortunately, Insert -> Indexes and Tables -> Indexes and Tables -> Insert Index/Table -> Entries lets you edit the default. Just eliminating the fill characters won't solve the problem, but eliminating them and positioning the page number closer to the table entry will. Better yet, position the page number before the table entry, which starts an indentation of 30-40 points.
Page dialogues include a default tab for headings and footers, plus an additional Borders and Background dialog that opens when you select the More button.
The Borders and Background dialog includes settings for adding lines to one or more sides of the header or footer. However, anything more than a single line, as thin as possible, is old-fashioned overkill. Even worse are a shadow (with your choice of color and distance from the header), and a colored background for the header or the footer.
In theory, LibreOffice's Gallery is a convenient way to store and access clipart.
However, in practice, it is less useful today unless you are stranded without a high-speed connection. Even more importantly, its default contents look like the graphic buttons, textures, and sounds that haven't been considered appropriate for a website—let alone a document—since 1998 or earlier.
If you think the Gallery is useful, locate its Path under Tools -> Options and delete all the default content. Then fill it with clipart that might actually be useful.
You can give both paragraphs and selected characters a border and a different background color—but the question is whether you should.
Regardless of whether you are working online or printing to paper, both backgrounds and borders are awkward, because you can't move them around. If you are doing layout that requires sideboxes or different backgrounds, you will be far less frustrated—and enjoy far more options—if you use text frames rather than paragraph or character formatting. In particular, text frames are far easier to move around and include wrap settings for other elements.
I don't mention these alleged features to criticize LibreOffice. The project inherited the code and can hardly be held responsible for parts of it becoming obsolete. To the contrary, LibreOffice has already reduced the size of the code in many areas and apparently plans on continuing the effort.
Still, any project is understandably reluctant to eliminate features, even if they are rarely used or have become things to avoid. I wouldn't mind in the least if my suggestions were taken up by those tidying the code.
However, more to the point, knowing what you should ignore can be useful for those who want to learn LibreOffice at an advanced level. Not only can the knowledge encourage best practices, but more to the point, it can help you focus on the features that are useful.
LibreOffice has some powerful features, particularly in Writer, which is more a desktop publisher than a word processor. However, finding those features can be difficult amid some of the clutter that the code has accumulated in the last three decades. Once you know where the clutter is, learning LibreOffice becomes both less of a task and less alarming.